PI Controller (Discrete or Continuous)

Discrete-time or continuous-time PI controller with external anti-windup input

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Libraries:
Simscape / Electrical / Control / General Control

Description

The Discrete PI Controller block implements discrete-time or continuous-time PI control with external anti-windup input.

This diagram shows the equivalent circuit for the controller with external anti-windup input.

Equations

The PI Controller (Discrete or Continuous) block calculates the control signal using the backward Euler discretization method:

$u(k)=\left[K_p+\left(K_i+du(k)K_{aw}\right)\frac{T_{s}z}{z-1}\right]\text{e}(\text{k}),$

where

• u is the control signal.

• K_p is the proportional gain coefficient.

• K_i is the integral gain coefficient.

• K_aw is the anti-windup gain coefficient.

• T_s is the sampling period.

• e is the error signal.

To prevent excessive overshoot, the block can use back calculation to implement an external anti-windup mechanism. It inputs du(k), the difference between the saturated control signal, u^sat(k), and the calculated unsaturated control signal, u(k). It then multiplies the difference by the anti-windup coefficient and adds the amplified signal from the integral gain.

Examples

DC Motor Control

A cascade speed-control structure for a DC motor. A PWM controlled four-quadrant Chopper is used to feed the DC motor. The Control subsystem includes the outer speed-control loop, the inner current-control loop, and the PWM generation. The total simulation time (t) is 4 seconds. At t = 1.5 seconds, the load torque increases. At t = 2.5 seconds, the reference speed is changed from 1000 rpm to 2000 rpm.

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Energy Balance in a 48V Starter Generator

An interior permanent magnet synchronous machine (IPMSM) used as a starter/generator in a simplified 48V automotive system. The system contains a 48V electric network and a 12V electric network. The internal combustion engine (ICE) is represented by basic mechanical blocks. The IPMSM operates as a motor until the ICE reaches the idle speed and then it operates as a generator. The IPMSM supplies power to the 48V network, which contains the R3 power consumer. The 48V network supplies power to the 12V network which has two consumers: R1 and R2. The total simulation time (t) is 0.5 seconds. At t = 0.05 seconds, the ICE turns on. At t = 0.1 seconds, R3 switches on. At t = 0.3 seconds, R2 switches on and increases the load on the 12V electric network. The EM Controller subsystem includes a multi-rate PI-based cascade control structure which has an outer voltage-control loop and two inner current-control loops. The task scheduling in the Control subsystem is implemented as a Stateflow® state machine. The DCDC Controller subsystem implements a simple PI controller for the DC-DC Buck converter, which feeds the 12V network. The Scopes subsystem contains scopes that allow you to see the simulation results.

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IPMSG Voltage Stabilization

Control an Interior Permanent Magnet Synchronous Generator (IPMSG) based low voltage generator system for a hybrid electric vehicle (HEV). The Control subsystem includes a multi-rate PI-based cascade control structure which has an outer voltage-control loop and two inner current-control loops. The task scheduling in the Control subsystem is implemented as a Stateflow® state machine. The Scopes subsystem contains scopes that allow you to see the simulation results. An ideal angular velocity source, which represents a combustion engine, drives the IPMSG. The IPMSG supplies low-voltage power to loads R1 and R2. At t = 0.4 seconds, the switch closes, increasing the load.

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Ports

Input

e — Error signal

scalar

Error signal, e(k), obtained as the difference between the reference, r(k), and measurement, y(k), signals.

Data Types: single | double

du — Control signal saturation

scalar

Difference, du(k), between the saturated u^sat(k) and the unsaturated control signals, u(k). If du(k) is zero, the anti-windup is disabled.

Description

Data Types: single | double

Reset — Integrator gain reset

scalar

External reset (rising edge) signal for the integrator.

Data Types: single | double

Output

u — Control signal

scalar

Control signal, u(k).

Data Types: single | double

Parameters

Proportional gain — K_p

1 (default) | positive scalar

Proportional gain, K_p, of the PI controller.

Integral gain — K_i

1 (default) | positive scalar

Integral gain,K_i, of the PI controller.

Anti-windup gain — K_aw

1 (default) | positive scalar

Anti-windup gain, K_aw, of the PI controller.

Integrator initial condition — Initial integrator value

0 (default) | scalar

Value of the integrator at simulation start time.

Sample time (-1 for inherited) — Block sample time

-1 (default) | 0 | positive scalar

Time between consecutive block executions. During execution, the block produces outputs and, if appropriate, updates its internal state. For more information, see What Is Sample Time? and Specify Sample Time.

For inherited discrete-time operation, set this parameter to -1. For discrete-time operation, set this parameter to a positive integer. For continuous-time operation, set this parameter to 0.

If this block is in a masked subsystem or a variant subsystem that supports switching between continuous operation and discrete operation, promote this parameter to ensure correct switching between the continuous and discrete implementations of the block. For more information, see Promote Block Parameters on a Mask.

References

[1] Åström, K. and T. Hägglund. Advanced PID Control. Research Triangle Park, NC: ISA, 2005.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2017b

R2025a: Support continuous-time simulation

The PI Controller (Discrete or Continuous) block now supports continuous-time simulation. For continuous-time operation, set the Sample time (-1 for inherited) parameter to 0.